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A Time-Homogeneous Diffusion Model with Tax

Part of:Markov processesApplicationsStochastic processesMathematical economicsSpecial processes

Published online by Cambridge University Press:  30 January 2018

Bin Li,
Qihe Tang and
Xiaowen Zhou
Bin Li*
Affiliation:
University of Iowa
Qihe Tang*
Affiliation:
University of Iowa
Xiaowen Zhou*
Affiliation:
Concordia University
*
∗ Postal address: Applied Mathematical and Computational Sciences Program, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242, USA. Email address: bin-li@uiowa.edu
∗∗ Postal address: Department of Statistics and Actuarial Science, University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, USA. Email address: qihe-tang@uiowa.edu
∗∗∗ Postal address: Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec, H3G 1M8, Canada. Email address: xzhou@mathstat.concordia.ca
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Abstract

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We study the two-sided exit problem of a time-homogeneous diffusion process with tax payments of loss-carry-forward type and obtain explicit formulae for the Laplace transforms associated with the two-sided exit problem. The expected present value of tax payments until default, the two-sided exit probabilities, and, hence, the nondefault probability with the default threshold equal to the lower bound are solved as immediate corollaries. A sufficient and necessary condition for the tax identity in ruin theory is discovered.

Keywords

Diffusionhitting timeLaplace transformMarkov propertytaxtwo-sided exit problem

MSC classification

Primary:62P05: Applications to actuarial sciences and financial mathematics
Secondary:60J60: Diffusion processes60G40: Stopping times; optimal stopping problems; gambling theory60K15: Markov renewal processes, semi-Markov processes91B30: Risk theory, insurance

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 1 , March 2013, pp. 195 - 207
Copyright
Copyright © Applied Probability Trust 2013 

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